Results obtained in 2008 :
In the orbit choice for the satellite GOCE (Gravity field and steady-state Ocean Circulation Explorer), one has to avoid proximity to a low order orbit resonance, for GOCE namely of the 16/1, because the same situation as appeared for the pair of satellites GRACE would repeat. During a pass through such a resonance, the density of the ground tracks decreases and in turn, also the precision of the „gravitational information“ derived from the measurements decreases. Moreover, for the measuring phases of the flight (measurements with the gradiometer), it is needed to select most stable orbits as for their minimum altitute variations due to a possible imperfect function of the drag-free system. We discuss the cases of resonant orbits 977/61 and 978/61.
In the area of the novel geodetic computational methodologies, an efficient program to compute normal equation matrices for the rigorous GOCE gravitational gradient analysis as well as the combination with other in-situ gravity observables has been developed. The efficient function setup of associated Legendre functions as well as inclination functions to an unlimited degree could be achieved. The use of lumped harmonic coefficients instead of the traditional approach enables spherical harmonic computations in spectral domain. Since the Legendre functions can be used without any resolution restriction by fast Fourier transform, the corresponding synthesis as well as analysis step on global data grids have been investigated with promising results. Finally, tests to combine in-situ gravity observables represented time-wise in the frequency domain with non-in-situ perturbation data through a common representation by means of lumped harmonics have been performed.
Concerning the item „Comparison of detailed satellite and terrestrial data“, a mathematical model for combination of heterogeneous gravity data was derived. The model is based on the external solution to the first (Dirichlet) boundary-value problem of the potential theory that links gravity observables (directional derivatives of the Earth’s gravitational potential) with unknown values of the gravitational potential (eventually numerical coefficients in a harmonic series expansion of the potential). Since the mathematical model can be used only if certain conditions are met, the “harmonicity” of the unknown gravitational potential (important for both the potential theory and the apparatus of harmonic series) in the entire solution domain was investigated. Observed data must be reduced for a gravitational effect of all masses outside the geoid (atmosphere and topography) that violate the “harmonicity” of the potential.
In April 2008 the new Earth’s Gravitational Model EGM 08 was released. It contains a set of spherical harmonic coefficients of the gravitational potential to degree and order 2190 that can be used for evaluation of various potential functionals with high accuracy and spatial resolution. Two such derivatives, the gravity anomaly and second-order radial derivative of the disturbing potential, were computed over selected areas with known impact craters. The displays of these derivatives clearly show not only the strong circular features known to be associated with these sites but other smaller symmetrical structures which appear to make them multiple impact sites. At Popigai, Siberia, the secondary circular features fall in a line from the primary. At Chicxulub, Yucatan, one secondary crater appears to be closely to the primary (both hidden under surface or under sea bottom).
Publications :
Bezděk A, Klokočník J, Kostelecký J, Floberghagen R, Gruber C (2009). Simulation of free fall and resonances in the GOCE mission. Accepted for publication in Journal of Geodynamics.
Tenzer R, Novák P (2008). Conditionality of inverse solutions to discretised integral equations in geoid modelling from local gravity data. Studia Geophysica et Geodaetica 52: 53-70.
Tenzer R, Ellmann A, Novák P, Vajda P (2008). The Earth’s gravity field components of the differences between gravity disturbances and gravity anomalies. In: Sideris M (Ed.) Observing our Changing Earth. Springer Berlin Heidelberg New York, ISBN 978-3-540-85425-8: 155-160.
Vajda P, Ellmann A , Meurers B, Vaníček P, Novák P, Tenzer R (2008). Global ellipsoid-referenced topographic, bathymetric and stripping corrections to gravity disturbance. Studia Geophysica et Geodaetica 52: 19-34.
Vajda P, Ellmann A , Meurers B, Vaníček P, Novák P, Tenzer R (2008). Gravity disturbances in regions of negative heights: A reference quasi-ellipsoid approach. Studia Geophysica et Geodaetica 52: 35-52.
Kadlec M, Kostelecký J, Novák P (2008). Database for evaluation of gravity field parameters in Central Europe. Geodetický a kartografický obzor 12: 282-288.
Klokočník J, Wagner CA, Kostelecký J, Bezděk A, Novák P, McAdoo D (2008) Variations in the accuracy of gravity recovery due to ground track variability: GRACE, CHAMP and GOCE. Journal of Geodesy 82: 917-927.
Novák P, Kostelecký J, Klokočník J (2008). On accuracy of current geopotential models estimated through a comparison of quasi-geoid models and GPS/levelling data. Studia Geophysica et Geodaetica (accepted, in print).
Tenzer T, Novák P, Prutkin I, Ellmann A, Vajda P (2008). Far-zone effects in direct gravity inversion by means of Molodensky's truncation coefficients. Studia Geophysica et Geodaetica (accepted, in print, in Czech).
Klokočník J, Kostelecký J, Novák P (2008). Chicxulub seems to be a double crater and Popigai has little brothers. Vesmír (accepted, in print, in Czech).
Novák P, Kostelecký J, Klokočník J (2008). The new global model of the Earth gravitational field EGM08. Geodetický a kartografický obzor (accepted).
Tsoulis D, Novák P, Kadlec M (2008). Evaluation of precise terrain effects using high-resolution digital elevation models. Journal of Geophysical Research (accepted).
Novák P (2008). Abel-Poisson integral in service of the geodetic inversion of gravity field observables. Journal of Geodesy (submitted).
Novák P (2008). High resolution constituents of the Earth gravitational field. Surveys in Geophysics (submitted).
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